I believe by cooling it with water it retains the copper softness , if let air cool it will get hard and not deform when recrushed properly.
~~~that hasn't been my experience Mutha=

. Let me explain. When I did this job again the other day, while in the middle of the process, and just after I got this washer cherry red, the phone rang, I set my work (the washer, and wire) down on the lift where my scooter sat. After the call ended and I came back to this job, it was obvious to me the washer had cooled so I proceeded by placing it on the drain fastener and I hand tightened it. I was called away again then this time when I returned I wanted to make sure I had tightened the drain bolt to at least the requisite torque so I looked up the torque value (online, easiest) and set my torque wrench for the highest of the two values given (low & high)
I was actually surprised to feel the washer give when tightened to the point my torque wrench clicked when the set torque was reached which told me two things. 1) my initial torque was low, 2) the washer returned to its original integrity despite not being dipped in water, AKA quenching, and the reason I posted the bit I did where I said it was necessary to use water to cool the work so one doesn't mistakenly burn thyself touching the hot metal
The only other people I've seen anneal copper is plumbers that use copper tubing as once they bend copper tube, if you try to bend it again, it feels like it hardens which it did so annealing is employed to allow the plumber to bend the tubing again if they didn't get the right amount of bend first time around. I've seen them spray water on the tubing to cool the tubing but I always thought they did that so they wouldn't burn themselves trying to work with hot tubing
I suppose you could experiment with this yourself or, if you feel it's necessary to quench the washer after heating it, go right ahead. I've been taught to cool the washer in water after heating it up and always figured it was part & parcel, "a requisite part of the process", until I found out different
It could also be that the washer in question (the one I used) was so small, that by heating it up and setting it on my metal lift, that the metal lift acted to quench the hot washer, like a giant metal heat sink, I don't know, I'm just guessing. I'd say this. If you feel,it's entirely necessary to quench your washer in water, then do so. It certainly won't hurt anything, and you can be sure once that hot copper hits the water, you aren't going to burn yourself=
Best,
Jake
Reddick Fla.
"The awkward part about an orgy is that afterwards, you're not too sure who to thank"
Bob Monkhouse